of this article the stable model will be applied to females only, though it may equally well be applied to males and with some complication to the two sexes together.
When the Honduras population of 1966 is considered as a sequence of cohorts, we note that those under 5 were born between mid-1961 and mid-1966; those 5 to 9 at last birthday between mid-1956 and mid-1961. Now, applying the stable model, if the population is increasing uniformly in the ratio X each 5 years, then the most recent cohort will have increased on the average for about 2Vz years since birth, or in the ratio A1/2; the cohort 5 to 9 in 1966 has been alive about ll/i years and would have increased in the ratio X3/2 . People who were bom in each earlier time would be related to the size of the population at that time in fixed ratio on the stable assumption. Moreover, some of them would have died in the meantime; with a fixed life table SL0//0 of the average annual births of the preceding 5 years are still alive in 1966; 5L5/1Q of the average of the 5 years before that, where
5 5Lx = / lx+tdt>
if 1X/1Q is the probability of surviving from birth to age x. Then it follows that in terms of this year's total of births B the number of survivors from the births of the last 5 years is the product B\~1/2 5/.0//0; of the 5 years before that is B\~3I2 5L5/10. . . . Thus the number under 15 would be the sum of the first three such quantities, the survivors of the three youngest cohorts, and the total number would be the sum of all such cohorts of which any members are now alive.
On this very simple way of looking at population, which assumes implicitly that all age-specific birth and death rates remain fixed, the percent of the population under age 1 5 would be
100 X
>-l/2 /• 4. \-3/2 r + \-5/2 i 4. A 5-^0 ^ A 5^5 ^ A 5^ 10
The ratio of increase X for Honduras at the 1966 age-specific birth and death rates would ultimately be 1.195 as we saw. A life table calculated from the same data provides us with the fact that
5LQ/1Q = 4.75394; SL5//0 = 4.57996; this corresponds to an annual rate r = 0.3564, or 35.64 per 1,000. (Such a rate r is thought of as compounded continuously, a device that considerably simplifies the mathematics and need not detain us here.) The birth rate for the stable condition corresponding to the Honduras regime of 1966 is 10006 = 44.05 and the death rate lOOOc/ = 8.41.